Tuning the bond-order wave phase in the half-filled extended Hubbard model

Abstract

Theoretical and computational studies of the quantum phase diagram of the one-dimensional half-filled extended Hubbard model (EHM) indicate a narrow bond order wave (BOW) phase with finite magnetic gap Em for on-site repulsion U < U * , the critical point, and nearest neighbor interaction Vc ≈ U/2 near the boundary of the charge density wave (CDW) phase. Potentials with more extended interactions that retain the EHM symmetry are shown to have a less cooperative CDW transition with higher U * and wider BOW phase. Density matrix renormalization group (DMRG) is used to obtain Em directly as the singlet-triplet gap, with finite Em marking the BOW boundary Vs(U ). The BOW/CDW boundary Vc(U ) is obtained from exact finite-size calculations that are consistent with previous EHM determinations. The kinetic energy or bond order provides a convenient new estimate of U * based on a metallic point at Vc(U ) for U < U * . Tuning the BOW phase of half-filled Hubbard models with different intersite potentials indicates a ground state with large charge fluctuations and magnetic frustration. The possibility of physical realizations of a BOW phase is raised for Coulomb interactions. PACS 71.10.Fd, 71.30.+h, 71.45.Lr PACS numbers: I.

Bond-order wave phase of the extended Hubbard model: Electronic solitons, paramagnetism, and coupling to Peierls and Holstein phonons

“…Quite unusually, E m increases with N at V = 2.5. DMRG calculations [10] of E m with PBC have minimum E m (N ) at N ≈ 30 for V = 2.2. Exact E m (N ) in Fig.…”

“…|Z N | = 0 is a metallic point at which P is not defined [31]; it corresponds to V c for U < U * and a continuous CDW transition [10]. The EHM has real Z and P = 0 by either C i or e-h symmetry.…”

“…DMRG with PBC provides an independent calculation [10] showing that E m (V ) opens at V s = 1.86t for the EHM with U = 4t. The gap is only 0.023t at V = 2.0 before reaching 0.241t at V = 2.10 and 0.63t at V = 2.20, just in the CDW phase.…”

“…Similarly, the V s boundary of a frustrated spin chain has been found [23] using E m (N ) = E σ (N ) up to N = 24. Multiple methods yield the boundary V c (N ) of the CDW phase [7,10]. The points V = V 1 (N ) in Table I or Fig.…”

“…The BOW/CDW boundary is at V c (U ) for U < U * , while the boundary to the spin-fluid phase with E m = 0 is at V s (U ) < V c (U ). Other half-filled 1D Hubbard models with spin-independent interactions have narrow BOW phases between the spin-fluid and CDW phases [10].…”